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Di-neutron clustering and deuteron-like tensor correlation in nuclear structure focusing on 11Li

11Li is a Borromean nucleus, where two out of three objects as 9Li + n and two neutrons independently do not form bound systems. Two neutrons should form a di-neutron cluster in the nuclear field generated by the 9Li core nucleus. We treat di-neutron clustering by solving the two neutron relative wave function precisely by using the bare nucleon-nucleon interaction so that the spatial clustering structure is obtained quantitatively within the whole 11Li nucleus. This di-neutron clustering is an essential dynamics to form the halo structure by making a compact di-neutron cluster, which distributes loosely around the 9Li core. The di-neutron clustering is a new concept and is a general phenomenon in neutron skin and neutron halo nuclei. This quantitative description of di-neutron clustering has made it necessary to consider another important deuteron-like tensor correlation, which is caused by strong tensor interaction in the nucleon-nucleon interaction. The tensor interaction originates from pion exchange and known to provide large attraction to form the 4He nucleus. The unique feature of the tensor correlation is to make highly correlated deuteron-like excitation, which interferes with shell model like structure in a unique way. This dynamical effect removes the magic number effect and makes easy the participation of the s-wave neutrons. Hence, there are pairing and deuteron-like tensor correlations in addition to the mean field structure in 9Li. The combined system of two additional neutrons with the correlated 9Li provides the halo phenomenon, in which the di-neutron clustering develops with the help of large s-wave component caused by the deuteron-like tensor correlation. In this lecture note, we would like to introduce these two new concepts in a systematic manner and fill a gap between the halo phenomenon and the microscopic reason for this interesting phenomenon.